Skip to content

IAI Actuarial Core Principles · Economic Modelling · Single and multifactor models for investment returns

A single-index model gives security returns R_i = a_i + b_i R_M + e_i. Security A has b = 1.2 and security B has b = 0.8. The market return variance is 0.0400 and residuals are uncorrelated with the market and with each other. What is the covariance between the returns of A and B?

The covariance is 0.0384. In a single-index model with uncorrelated residuals, covariance equals the product of the two betas and the market variance: 1.2 × 0.8 × 0.04 = 0.0384.

  1. A0.0192
  2. B0.0384Correct
  3. C0.0400
  4. D0.0960
  5. 0.0480

Explanation

Under the single-index model Cov(A,B) = b_A × b_B × Var(R_M), since the residuals are uncorrelated. That is 1.2 × 0.8 × 0.04 = 0.96 × 0.04 = 0.0384. The value 0.0192 comes from wrongly halving the result, while 0.0960 omits the market variance scaling incorrectly.

Did you get it right without looking?

One question tells you little. A timed set on Single and multifactor models for investment returns shows your real accuracy, how long you take and where you lose marks.

Practise Single and multifactor models for investment returnsFree diagnostic mock

More Single and multifactor models for investment returns questions